‌dx We can write ‌sin‌x+8‌cos‌x=A(4sin‌x+6‌cos‌x) ‌‌‌+B‌
d
dx
(4sin‌x+6‌cos‌x) ‌sin‌x+8‌cos‌x ‌=A(4sin‌x+6‌cos‌x)+B(4‌cos‌x−6sin‌x) On equating the coefficient of sin‌x and cos‌x, we get ‌1=4A−6B,‌‌8=6A+4B ‌⇒‌‌A=1,B=‌